Question

Diazapam is a drug, its metabolic decay follows first order reaction rate law. You have observed that it takes 4 days (96 hours) in the patients body for a 5mg dose to be reduced to 1mg.

A. calculate the rate constant and halflife of diazapam in the body.

B. A patent requires a minimum amount of 1.5mg od Diazapam at any given time, and you decide to precribe 2mg tablets. when should the patient take the second dose?

C. when should the patent take the third dose?

Answer 1

Reaction law: It defines the rate of conversion from reactant into the product.

1. It is given in the question that diazepam drug is introduced to the patient body, initial concentration is C_o(5mg), it follows first-order reaction law. The final concentration of the drug is C_f(1mg) in time(t)(96 hours).

Then, according to first order reaction law:

C=C₀ * e^-t or ln(C) = -λt + ln(C0)

ln (5) – ln (1) = λ*96

λ = ln (4)/96

Rate (λ) = 1.386/96 = 0.0144

However, first order reaction is independent to the initial concentration.

So,

T_1/2 = ln(2)/ λ = 0.693/0.0144 = 48 hour